the Bochner integral for \(L^p_a(dA_\alpha )\) . As in the proof of Theorem 1 to show that
the equality (3) is valid for all \(z\in \mathbb {D}\)  we shall prove the continuity of its left-hand side. To this end we shall prove that for every \(z_0\in \mathbb {D}\)  and for every compact neighborhood \(U\subset \mathbb {D}\)  of \(z_0\)  there is a \(dA\)  integrable majorant
for the integrand of the left-hand side of (3). First note that by [1]} there is a constant \(C>0\)  such that for \(f\in L^p_a(dA_\alpha ),z\in \mathbb {D}\)
\(|f(z)|^p\le \frac{C}{(1-|z|^2)^{2+\alpha }}\Vert f\Vert ^p_{p,\alpha }.\) 
